I have a Norhtec MicroClient Jr miniature computer for sale. These are very power efficient(less than most desktops running on standby), tiny(about the size of two packets of fags) and almost completely silent.
They use compact flash cards, USB memory sticks or conventional hard disks to run whatever operating system you like. I will provide it with Puppy Linux installed on a memory stick for an extra £5 if you want to use it as a power efficient web browser, but that's just a starting point - it's the kind of thing you could find all kinds of uses for if you were inventive. It's got an American plug on its power supply, but I've run it through an adaptor, which I will include for free.
Be the envy of all your nerdy friends and do something in the warm after your ride!
Full specs at http://www.norhtec.com
This was really expensive, as the price on their website doesn't include shipping or import duty. So at £80 is an absolute bargain, but I'm off travelling soon so make an offer, it has to go and I'm not easily offended!
I also have a MicroClient Sr. This is externally identical, but has a more powerful processor and more RAM. £120 posted.